Which set of measurements could be the side lengths of a triangle?

a.)3m, 6m, 3m
b.)4m, 7m, 12m
c.)9m, 5m, 3m
d.)4m, 11m, 9m

answer:

syd is 23 and dev is 69

step-by-step explanation:

let dev's age be x and syd's age be y

since dev is 3 times older than syd, we may write  

x

=

3

y

since the sum of their ages is 92, we may write  

x

+

y

=

92

now replacing x with 3y, we get :  

3

y

+

y

=

92

hence  

y

=

92

4

=

23

and so syd is 23 year old.

back substituting we get dev is 69 years old.

answer:

second choice

step-by-step explanation:

the unknown leg x in right triangle is opposite to the angle of the measure 70°.

use the definition of the sine of the angle:

hence,

answer:

first option. f(x) has no zeroes

second option. f(x) has a period of 2π.

step-by-step explanation:

1) the function sec(x) is the inverse of the cosine function:

this function has no zeroes, because:

it can not be equal to zero

then the first option is true.

2) as the secant function is the inverse of the cosine function, it has the same period 2π, then the second option is true.

3) the cosine function has an amplitude of 1, but the secant function does not, then the third option is false.

4) the secant function is symmetric about the y-axis, but not about the origin, then the fourth option is false.

5) the asymptotes of the secant funtion are where the cosine function is equal to zero, this is at integer multiples of π/2, then 5the fifth option is false.